Supplementary data:

Van-der-Waals-gap tunneling spectroscopy for single-wall carbon

nanotubes

Dong-Hwan Choi, Seunghun Jang, Du-Won Jeong, Jeong-O Lee, Hyunju Chang, Dong-Han

Ha, Seung Mi Lee, Jongwoo Kim, Yung Doug Suh, Myung-Ho Bae and Ju-Jin Kim

Section 1. Sample preparation

1-1. Growth of CNTs

(1) Positioning markers were pattered on a 500 nm thick SiO2/Si substrate by Cr (5 nm)/Au (30 nm) metal layers.

(2) A catalyst liquid composed of CH3OH:(Fe(NO3)3)9H2O: Al2O3: MoO2 = 15:20:15:5 (mg) was dropped on a PMMA widow (2 μm×2 μm) defined in the center of the substrate.

(3) After waiting for ~20 sec, the liquid was blown by a nitrogen gas. The PMMA layer was washed out by acetone after annealing process at 150 oC for 3 min for stabilization of the catalyst.

(4) In a CVD furnace, CNTs are grown while a gas mixture composed of CH4:H2 = 5000:500 (sccm) at 915 oC for 10 min.

(5) The grown CNT is located by AFM with the positioning markers.

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1-2. Deposition of indium electrodes on SWCNT

Indium was deposited by a thermal evaporator to define electrodes on a SWCNT after electron beam lithography on a PMMA layer and develop process. The sample was loaded into the evaporator and the pressure of the chamber was lowered to ~10 -6 Torr at room temperature. The sample stage was cooled from room temperature to 100 K for 1.5 hours by liquid nitrogen. We note that the sample was not heated over room temperature through entire process. During cooling process, the chamber pressure was more lowered as ~3×10-7 Torr. This is because a cold body (OFHC block, 120 mm×120 mm with thickness of 20 mm), where liquid nitrogen flows through the inside, plays as an impurity collector. Since the surface area of the metal block is much larger than the substrate (size: 5×5 mm), which was attached at the middle of the metal-block bottom, and the block temperature was lower than that of sample substrate due to the thermal gradient during cool-down, we believe that the wall of the block will collect most of impurities. To check the interface properties, we fabricated the Pd-contacted SWCNT devices with the same cooling method, which showed the ideal low-resistance ohmic contacts contrary to In-contacted devices. The ideal contacts with Pd with the same cold substrate show that the possible impurity adsorptions on the cold

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Figure S1. Atomic force microscope (AFM) images of indium films deposited on SiO2 layers with different temperature conditions of the sample holder (Tstage) in a thermal evaporator: (a) no cooling, (b) 200 K, (c) 150 K and (d) 100 K, where lower panels show height profiles along dashed lines in corresponding figures.

0 1 2 3 4 5 60

50

100

x (m)

Hei

ght (

nm)

0 1 2 3 4 5 60

50

100

Hei

ght (

nm)

x (m)

0 1 2 3 4 5 60

50

100

x (m)

Hei

ght (

nm)

0 1 2 3 4 5 60

50

100

x (m)

Hei

ght (

nm)

a: No cooling process b: Tstage = 200 K

c: Tstage = 150 K d: Tstage = 100 K

substrate are not crucial effect on the performance of our devices. The temperature of the sample stage was kept at 100 K during the evaporation process. After indium deposition, the sample was thermally cycled to room temperature under the pressure of ~10 -6 Torr for the successive fabrication process. And, the completed sample was again cooled to 4.2 K in a measurement system for the electrical measurements. Figure S1 shows AFM images of 60 nm thick indium electrodes deposited on SiO2 substrates with different temperatures of the sample holder (metal box) in a thermal evaporator. Without any cooling process in Figure S1a, indium grains with a size of ~ 0.5 μm are separated from each other, resulting in no current flowing through the indium electrodes. With lowering temperature in Figs S1a-S1d, the grain size of indium and gap between the grains are reduced and finally they form a homogeneous indium film at T = 100 K.

Section 2. Characterization of Single-wall CNTs

2-1. SWCNT diameters estimated from radial breathing mode and AFM images

Figure S2. (a) Radial breathing mode of a SWCNT obtained by two independent measurements with a 514 nm laser. (b) Left: AFM amplitude image of the SWCNT used for the Raman spectrum of (a). Right: a magnified image of a red-boxed region in the left image. (c) Height profiles of CNTs along three vertical lines in the right image of (b).

After growing the SWCNT, we obtained the radial breathing mode (RBM) of a single-wall CNT (SWCNT) at νRBM=¿232 ~ 236 cm-1, as shown in Figure S2a. The diameter (D) was estimated by the frequency of the RBM peak as 1.05 ~ 1.07 nm, with a relation of

νRBM=248 cm−1∙ nmD

[1]. Figures S2b and S2c show AFM images taken before nano-

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150 200 250

8

10

12

14

16

18

Inte

nsity

(a.u

.)

Raman shift (cm-1)

236 cm-1: 1.05 nm

0.0 0.1 0.2 0.3 0.40.0

0.5

1.0

1.5

Hei

ght (

nm)

x (m)0.0 0.1 0.2 0.3 0.4

0.0

0.5

1.0

1.5

Hei

ght (

nm)

x (m)0.0 0.1 0.2 0.3 0.4

0.0

0.5

1.0

1.5

Hei

ght (

nm)

x (m)

(i) (ii) (iii)

(i) (ii) (iii)

1.08 nm 1.08 nm 1.06 nm

232 cm-1: 1.07 nm

a b

c

2 m

fabrication process and corresponding height profiles, respectively. The measured SWCNT diameter of 1.06 ~1.08 nm is consistent with that estimated by the RBM signal. Actually, for working samples, however, we did not perform the Raman measurement before electrical measurement because of worrying about contamination to the SWCNTs. But, after deposition of electrodes and performing electrical measurements, it was hard to get the RBM signal. Thus, we adopted the SWCNT diameters measured by AFM, which were taken before nano-fabrication process.

Figure S3. (a) AFM amplitude image (taken before nano-fabrication process) of the sm-SWCNT of Figure 3a in the main panel. (b) Height profiles along dashed lines indicated by (i) and (ii) in a). (c) AFM amplitude image of the completed sm-SWCNT device.

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0 1 2

0.0

0.5

1.0

Hei

ght (

nm)

x (m)

(ii)

1.16 nm

0 1 2 3

0.0

0.5

1.0

Hei

ght (

nm)

x (m)

(i)

1.06 nm

(i)(ii)

a c

b

2 m 1 m

0.0 0.5 1.0

0.0

0.5

1.0H

eigh

t (nm

)

x (m)

(ii)

1.1 nm

0.0 0.5 1.0

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1.0

Hei

ght (

nm)

x (m)

(i)

1.1 nm

(i)(ii)

a c

b

2 m 2 m

1500 2000 2500 30000

100

200

300

400

500

600

Inte

nsity

(a.u

.)

Raman shift (cm-1)

d

Figure S4. (a) AFM amplitude image (taken before nano-fabrication process) of the m-SWCNT of Figure 3c in the main panel. (b) Height profiles along dashed lines indicated by (i) and (ii) in a). (c) AFM amplitude image of the completed m-SWCNT device. (d) Raman data of the m-SWCNT taken at the location indicated by an arrow in (c), which shows pronounced G and 2D peaks at 1591 and 2680.6 cm-1, respectively.

2-2. Comparison between sm-SWCNT and m-SWCNT

Figure S5. (a) dI/dVsd-Vsd curves of the sm-SWCNT for selected Vbg, which were replotted from Figure 3(a). It shows zero conductance for -0.1 V < Vsd < 0.4 V as a representative sm-SWCNT character. (b) dI/dVsd-Vsd curves of m-SWCNT for selected Vbg, which were replotted from Figure 3(c). It shows finite conductance between the conductance peaks corresponding to the first subbands as a representative m-SWCNT character.

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-1.0 -0.5 0.0 0.50

2

4

dI/d

Vsd

(nS

)

Vsd (V)

-60 -50 -40 -30 -20 -10 0 10 20

Vbg (V)

-0.6 -0.3 0.0 0.3 0.60

2

4

dI/d

Vsd

(nS

)

Vsd (V)

-50 -40 -20 0

Vbg (V)

a b

Section 3. Another sm-SWCNT device

Figure S6. (a) AFM amplitude image of another sm-SWCNT device (taken before nano-fabrication process), where the SWCNT segment with two metal electrodes denoted by two dashed rectangles was tested. (b) Height profiles along dashed lines indicated by (i), (ii), (iii) and (iv) in (a). D of this sm-SWCNT is in 1.21 ~ 1.3 nm. (c) AFM amplitude image of the completed sm-CNT device (L = 1.5 μm).

Figure S7. (a) dI/dVsd map of sm-SWCNT of Figure S10. (b) I-Vsd and dI/dVsd-Vsd curves at Vbg = 50 V. The I-Vsd curve for Vsd < 0 V shows step-like curves, which correspond to conductance peaks in

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0.0 0.5 1.0 1.5

0.0

0.5

1.0

1.5H

eigh

t (nm

)

x (m)

(iii)

1.3 nm

2 m0.0 0.5 1.0 1.5

0.0

0.5

1.0

1.5

Hei

ght (

nm)

x (m)

(i)

1.24 nm

0.0 0.5 1.0 1.5

0.0

0.5

1.0

1.5

Hei

ght (

nm)

x (m)

(ii)

1.21 nm

0.0 0.5 1.0 1.5

0.0

0.5

1.0

1.5

Hei

ght (

nm)

x (m)

(iv)

1.24 nm

2 m

(i)(ii)

(ii)(iv)

a b

c

-1.0 -0.5 0.0 0.5 1.0-0.8

-0.4

0.0

0.4

0.8

Vsd (V)

I (A

)

0

1

2

3

4

dI/d

Vsd

(S

)

0 10 20 30 40 50 60-0.9

-0.6

-0.3

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0.6

0.9

Vsd

(V)

Vbg (V)-1.0 -0.5 0.0 0.5 1.0

-4

-2

0

2

DO

S (a

.u.)

dI/d

Vsd

(S

)

Vsd (V)

(11, 6) D = 1.17 nm

(11, 7) D = 1.23 nm

(12, 7) D = 1.3 nm

0 10 20 30 40 50 60-0.9

-0.6

-0.3

0.0

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0.6

0.9

Vbg (V)

Vsd

(V)

-1.0 -0.5 0.0 0.5 1.0

-4

-2

0

2

DO

S (a

.u.)

dI/d

Vsd

(S

)

Vsd (V)-1.0 -0.5 0.0 0.5 1.0

-0.8

-0.4

0.0

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Vsd (V)

I (A

)

0

1

2

3

4

dI/d

Vsd

(S

)

(11, 6) D = 1.17 nm

(11, 7) D = 1.23 nm

(12, 7) D = 1.3 nm

0 1.5dI/dVsd (μS)

0 1.5dI/dVsd (μS)

a b c

d e f

dI/dVsd-Vsd curve. (c) The same plot of b) (a black curve) with three calculated DOS structures for the comparison. Chiral indices are (12, 7), (11, 7) and (11, 6) having D = 1.17 ~ 1.3 nm, which are in a range measured by AFM in Figure S6. The locations of subband edges are consistent with Vsd

corresponding to conductance peaks. (d)-(f) Electrical-transport results of the same sm-SWCNT of (a), but the source and drain electrodes were physically swapped. The dI/dVsd map and I-Vsd curve was inverted in Vsd including conductance peaks, which indicates that the potential drop across the contacts is asymmetric. For instance, we always see the tunneling process at the same contact having higher tunneling resistance regardless of the electrical configuration.

Section 4. Computational details

To study the atomic and electronic structures of the indium (In)/SWCNT interfaces, we use Vienna Ab initio simulation package (VASP) [2],[3]. The exchange–correlation functional was approximated using the Perdew–Burke–Ernzerhof (PBE) expression [4]. Specifically, the optB86b-vdW functional, implemented in VASP by Klimeš et al. to account for weak van der Waals (vdW) interactions, was used for all the calculations [5]. Electron–ion interactions were modeled using the projector-augmented wave (PAW) method [6]. The electronic wave functions were expanded in a basis set of plane waves with a kinetic energy cutoff of 500 eV. Geometry relaxation steps were performed under the criterion that the ionic forces were reduced below 0.02 eV/Å. The minimal unit cell of the isolated (8,0) SWCNT is used for the unit cell along the axial direction (x) of the metal/(8,0) SWCNT system. The lattice mismatch between the metal surface and the (8,0) SWCNT along the SWCNT axis results in 6.9 % compressed In(110) and 3.7 % expanded Pd(111) surfaces, compared with the experimental values [7]. In all interface models studied in this work, at least 20 Å vacuum regions along the perpendicular direction (z) to the two-dimensional slab are included to minimize the interaction between neighboring image cells.

Section 5. Pd / (8,0) SWCNT contact model calculations

We have performed additional DFT calculations on palladium (Pd)/(8,0) SWCNT contact model, as an well-known example of strong chemisorption interface. As shown in the optimized structure of Pd/SWCNT contact model of Figure S8a, the distance between carbon atom and Pd metal atom is about 2.04 Å. The large amount of charge transfer from SWCNT to Pd was also found in Figure S8b, as expected from the strong chemical bonding between -orbitals of carbon and d-orbitals of Pd [8]. This strong chemical bonding results in altering the electronic structure of (8,0) SWCNT after Pd contact, as shown in PDOS plot in Figure S8c. The semiconducting properties of (8,0) SWCNT completely disappear after Pd contact, which is agree well with the previous calculations [9].

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Figure S8. (a) A cross-sectional side view of the optimized geometries for Pd/(8,0) SWCNT contact. The bluish green, and gray balls represent Pd, and C atoms, respectively. (b) XY-averaged charge density differences for Pd/(8,0) SWCNT contact is plotted along the perpendicular direction (z) to the Pd(111) surface. Charge density difference for Pd/SWCNT contact is averaged over the dotted blue boxes as shown in a). (c) Calculated projected density of states (PDOS) for (8,0) SWCNT in contact with the Pd(111) surface. In C, the Fermi levels are set to zero, and the red dotted line represents the PDOS for the isolated SWCNT system.

Section 6. Calculation for the tunneling probability

With our calculation results of the XY-averaged electrostatic potentials, we can calculate the transmission probability using the Wentzel–Kramers–Brillouin (WKB) approximation [10]. The tunneling probability P can be numerically calculated as:

P=exp[−2 β √2 mUℏ s ] ,

where the average potential is:

U =1s∫s1

s2

U ( z ) dz ,

the dimensionless correction factor is:

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β=1− 18U 2 s

∫s1

s2

[U ( z )−U ]2dz ,

and m is the electron mass. s1 And s2 represent the start and the end point of the potential, respectively.

References for supplementary Information

[1] M.S. Dresselhaus, G. Dresselhaus, A. Jorio, A.G.S. Filho, R. Saito, Raman spectroscopy on isolated single wall carbon nanotubes, Carbon. 40 (2002) 2043–2061.

[2] G. Kresse, J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B. 47 (1993) 558–561.

[3] G. Kresse, J. Furthmu, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set ¨, Phys. Rev. B. 54 (1996) 11169.

[4] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77 (1996) 3865–3868.

[5] J. Klimes, D.R. Bowler, A. Michaelides, Chemical accuracy for the van der Waals density functional, J. Phys. Condens. Matter. 22 (2010) 022201.

[6] P. E. Blochl, Projector augmented-wave method, Phys. Rev. B. 50 (1994) 17953.[7] C. Kittel, Introduction to Solid State Physics, Wiley, vol. 7th ed (1996).[8] C. Gong, G. Lee, B. Shan, E.M. Vogel, R.M. Wallace, K. Cho, First-principles study

of metal – graphene interfaces, J. Appl. Phys. 108 (2010) 123711.[9] W. Zhu, E. Kaxiras, The Nature of Contact between Pd Leads and Semiconducting

Carbon Nanotubes, Nano Lett. 6 (2006) 1415–1419.[10] J.G. Simmons, Generalized Formula for the Electric Tunnel Effect between Similar

Electrodes Separated by a Thin Insulating Film, J. Appl. Phys. 34 (1963) 1793.

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